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Self-adjoint Extensions of Restrictions

- A. Posilicano
- Mathematics
- 27 March 2007

We provide a simple recipe for obtaining all self-adjoint extensions, together with their resolvent, of the symmetric operator $S$ obtained by restricting the self-adjoint operator… Expand

A Krein-like Formula for Singular Perturbations of Self-Adjoint Operators and Applications

- A. Posilicano
- Mathematics
- 9 May 2000

Abstract Given a self-adjoint operator A : D ( A )⊆ H → H and a continuous linear operator τ : D ( A )→ X with Range τ ′∩ H ′={0}, X a Banach space, we explicitly construct a family A τ Θ of… Expand

Boundary triples and Weyl functions for singular perturbations of self-adjoint operators

- A. Posilicano
- Mathematics
- 4 September 2003

Given the symmetric operator $A_N$ obtained by restricting the self-adjoint operator $A$ to $N$, a linear dense set, closed with respect to the graph norm, we determine a convenient boundary triple… Expand

On the spectral theory of Gesztesy–Šeba realizations of 1-D Dirac operators with point interactions on a discrete set

- R. Carlone, M. Malamud, A. Posilicano
- Mathematics
- 20 February 2013

On inverses of Krein's Q-functions

- C. Cacciapuoti, Davide Fermi, A. Posilicano
- Mathematics
- 13 September 2018

Let $A_{Q}$ be the self-adjoint operator defined by the $Q$-function $Q:z\mapsto Q_{z}$ through the Krein-like resolvent formula $$(-A_{Q}+z)^{-1}= (-A_{0}+z)^{-1}+G_{z}WQ_{z}^{-1}VG_{\bar… Expand

Krein's resolvent formula for self-adjoint extensions of symmetric second-order elliptic differential operators

- A. Posilicano, L. Raimondi
- Mathematics
- 21 April 2008

Given a symmetric, semi-bounded, second-order elliptic differential operator A on a bounded domain with C1,1 boundary, we provide a Kreĭn-type formula for the resolvent difference between its… Expand

Self-adjoint elliptic operators with boundary conditions on not closed hypersurfaces

- A. Mantile, A. Posilicano, M. Sini
- Mathematics
- 27 May 2015

Wave equations with concentrated nonlinearities

- D. Noja, A. Posilicano
- Mathematics
- 18 November 2004

In this paper, we address the problem of wave dynamics in the presence of concentrated nonlinearities. Given a vector field V on an open subset of and a discrete set with n elements, we define a… Expand

Finite speed of propagation and local boundary conditions for wave equations with point interactions

- P. Kurasov, A. Posilicano
- Mathematics
- 25 April 2005

We show that the boundary conditions entering in the definition of the self-adjoint operator Delta(A,B) describing the Laplacian plus afinite number of point interactions are local if and only if the… Expand

On the Self-Adjointness of H+A∗+A

- A. Posilicano
- Mathematics
- 11 March 2020

Let $H:D(H)\subseteq{\mathscr F}\to{\mathscr F}$ be self-adjoint and let $A:D(H)\to{\mathscr F}$ (playing the role of the annihilator operator) be $H$-bounded. Assuming some additional hypotheses on… Expand

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